This page is www.math.columbia.edu/~bayer/S05/linalg

Section 002 (Bayer)
Tuesdays and Thursdays, 11:00am-12:15pm
323 Milbank Hall (Barnard)

Dave Bayer (x42643, 426 Mathematics, www.math.columbia.edu/~bayer)
Bulletin page | Directory of Classes : Mathematics
Student Services Online

Email

My email address is  

Please include the phrase "Linear Algebra Spring 2005" in the subject line of any correspondence with me concerning this course.

Office Hours

Exams

There will be two exams (30 points each) and a final (40 points). The final is not cumulative.

These dates do not coincide with any religious holiday which causes suspension of New York City's alternate side parking regulations; see NYC Parking Calendar. Please discuss other conflicts with me well in advance of the exam in question.

Master University Examination Schedule
University Academic Calendar

Text: Linear Algebra with Applications Sixth Edition, by Steven J. Leon. Prentice Hall, 1998, ISBN 0130337811. University bookstore ($105) or AddALL ($45 and up). This semester we will cover chapters 1, 2, 3, 4, 5, 6.

Teaching Assistants

The teaching assistant for this course is Eric Simring ( simring@math.columbia.edu).

Course materials

Course materials will be posted in Acrobat 4 PDF format (PDF 1.3). Your browser can be trained to automatically open these files with Acrobat Reader, a free program which you can download from (If you have trouble reading or downloading these files, check to see if you're using an outdated version of Acrobat, and upgrade to the latest version, or try using a different computer.)

Course materials from previous semesters

I have taught this course before; you may be able to find further practice materials on the web pages from previous semesters:

Homework Assignments

  1. Matrices and Systems of Equations
    1. Systems of Linear Equations. Exercises 1-8
    2. Row Echelon Form. Exercises 1-3, 5, 6
    3. Matrix Algebra. Exercises 1-10, 12, 20
    4. Elementary Matrices. Exercises 1-5, 7, 9
  2. Determinants
    1. The Determinant of a Matrix. Exercises 1-4, 6
    2. Properties of Determinants. Exercises 1, 3, 4, 7, 10
    3. Cramer's Rule. Exercises 1-6
  3. Vector Spaces
    1. Vector Spaces. Exercises 1-10
    2. Subspaces. Exercises 1-8
    3. Linear Independence. Exercises 1-9
    4. Basis and Dimension. Exercises 1-8, 11
    5. Change of Basis. Exercises 1-5, 8-10
    6. Rowspace, column space. Exercises 1-7
  4. Linear Transformations
    1. Linear transformations, definitions and examples. Exercises 1, 3-5, 12
    2. Matrix representation of linear transformations. Exercises 1-5
    3. Similarity. Exercises 1, 3-6
  5. Orthogonality
    1. The scalar product. Exercises 1-8
    2. Orthogonal subspaces. Exercises 1, 2
    3. Inner product spaces. Exercises 1-4
    4. Least squares problems. Exercises 1-6
    5. Orthonormal sets. Exercises 1, 2, 4, 7, 8
    6. The Gram-Schmidt orthogonalization process. Exercises 1-4
  6. Eigenvalues
    1. Eigenvalues and eigenvectors. Exercises 1-5
    2. Systems of linear differential equations. Exercise 1
    3. Diagonalization. Exercises 1-4
    4. Hermitian matrices. Exercises 1, 4
    5. Quadratic forms. Exercises 1, 3
    6. Positive definite matrices. Exercises 1, 3, 4

Calendar

Monday Tuesday Wednesday Thursday Friday
17 Jan 05
 18
1.1 		19
 20
1.2 		21
24 Jan
 25
1.3 		26
 27
1.4, 1.5 		28
31 Jan
 1 Feb
2.1 		2
 3
2.2 		4
7 Feb
 8
2.3 		9
 10
Review 		11
14 Feb
 15
Exam 		16
 17
3.1 		18
21 Feb
 22
3.2
Last day to drop 		23
 24
3.3 		25
28 Feb
 1 Mar
3.4, 3.5 		2
 3
3.6 		4
7 Mar
 8
4.1 		9
 10
4.2 		11
14 Mar
Spring break 		15
 16
 17
 18
21 Mar
 22
4.3 		23
 24
Review 		25
28 Mar
 29
Exam 		30
 31
5.1, 5.2 		1 Apr
4 Apr
 5
5.3 		6
 7
5.4, 5.5 		8
11 Apr
 12
5.6 		13
 14
6.1, 6.2 		15
18 Apr
 19
6.3 		20
 21
6.4, 6.5 		22
25 Apr
 26
6.6 		27
 28
Review 		29
2 May
Last day of classes 		3
 4
 5
 6
First day of exams
9 May
 10
FINAL
(Projected) 		11
 12
 13
Last day of exams